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Question

The amount of pollution content added in air in a city to $$x$$ diesel vehicles is given by $$P(x) = 0.005x^3+0.02x^2+30x$$. Find the marginal increase in pollution content when $$3$$ diesel vehicles are added.


Solution

$$P(x)=0.005x^3+0.02x^2+30x$$
Differentiating w.r.t to x we get,
$$P'(x)=3(0.005)x^2+2(0.02)x+30$$
$$P'(3)=3\times 0.005(3)^2+2(0.02)(3)+30$$
$$P'(3)=30.255$$

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